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Which RCV-IRV? — Hare and the Other Sequential-Elimination Methods

Once you say "RCV-IRV," the next question is which one. "Instant runoff" names a shape — rank the ballots, eliminate, transfer, repeat — but the elimination rule and the ballot rules still have to be pinned down, and different choices crown different winners on the very same votes.

How the methods divide (family tree)

Every method below reads the same ranked ballot; they differ in what they do with it. ✅ marks the Condorcet-safe methods (always elect the head-to-head winner); ❌ marks Hare's center squeeze.

graph LR
    %% LR, not TD: the 12 leaves stack vertically, keeping the diagram ~4 node-columns
    %% wide — a TD layout is ~2300px wide and gets shrunk to unreadable on the site.
    R["RANKED BALLOT<br/>voter orders<br/>the candidates"]

    R --> SEQ["Sequential elimination<br/>(instant-runoff shape)"]
    R --> PW["Pairwise / Condorcet<br/>(no elimination)"]
    R --> POS["Positional<br/>(no elimination)"]
    R --> MW["Multi-winner<br/>(proportional)"]

    SEQ --> F1["eliminate by<br/>FEWEST first choices"]
    SEQ --> FL["eliminate by<br/>MOST last choices"]
    SEQ --> FB["eliminate by<br/>lowest BORDA score"]
    SEQ --> FH["eliminate loser of<br/>BOTTOM-TWO runoff"]

    F1 --> HARE["RCV-IRV (Hare)<br/>= US 'RCV' ❌ squeeze"]
    F1 --> BATCH["Batch elimination"]
    F1 --> CONT["Contingent / Supplementary<br/>one round, top-two"]
    FL --> COOMBS["Coombs"]
    FB --> BALD["Baldwin ✅"]
    FB --> NAN["Nanson ✅"]
    FH --> BTR["BTR-IRV ✅"]

    PW --> RR["Ranked Robin /<br/>Copeland ✅"]
    PW --> CMORE["Schulze · Ranked Pairs ·<br/>Minimax ✅"]
    POS --> BORDA["Borda"]
    POS --> BUCK["Bucklin"]
    MW --> STV["STV — Hare,<br/>proportional"]

    %% stroke-only highlighting: hard-coded fills break dark mode (the site theme
    %% controls label color, so light fills get light text); borders work in both.
    classDef safe stroke:#4caf50,stroke-width:3px;
    classDef squeeze stroke:#e57373,stroke-width:3px;
    class BALD,NAN,BTR,RR,CMORE safe;
    class HARE squeeze;

The whole tree is ranked voting. Score/rate methods — STAR, Approval, Score — sit outside it entirely (voters rate rather than order), which is why they aren't on this chart. The single split that matters most: methods that eliminate on first choices (Hare, Contingent) can squeeze the center; methods that read the whole ballot (Borda-elim, BTR, and the Condorcet family) don't.

The default: RCV-IRV (Hare)

Unless someone says otherwise, "RCV" in the US means IRV under the Hare rule (after Thomas Hare): tally first choices; if a candidate has more than half, they win; otherwise eliminate the candidate with the fewest first choices, transfer each of those ballots to its next still-standing choice, and repeat until someone holds a majority of the remaining active ballots (or only two candidates are left). Everything below is a variation on that — either a different rule for who gets eliminated, or a different rule for how the ballots are read.

Variants that change who gets eliminated

These keep the "instant runoff" shape but swap the elimination rule. They read an identical ranked ballot and can elect different winners.

Variant Elimination rule Condorcet-safe? Seen in the wild Page
Hare (standard IRV) drop the candidate with the fewest first-place votes, one per round No (center squeeze) US "RCV": Maine, Alaska, NYC, SF… Hare
Batch elimination drop all candidates who are mathematically out of reach at once Same winner as Hare in most cases; can differ at the margins North Carolina statute; speeds hand counts Hare § batch
Contingent vote one round only — eliminate everyone except the top two, then transfer No Sri Lanka presidency (rank up to 3) Contingent & SV
Supplementary vote contingent vote with the ballot limited to 1st + 2nd choice No London Mayor / English PCCs until 2022 (now first-past-the-post) Contingent & SV
Bottom-Two-Runoff (BTR-IRV) each round, the two lowest candidates meet head-to-head; the loser is eliminated Yes — a Condorcet winner can never be cut proposed reform (Rob LeGrand, 2006) BTR
Coombs drop the candidate with the most last-place votes, each round No, but resists center squeeze rare; classroom / academic Coombs
Baldwin drop the candidate with the lowest Borda score, each round Yes academic Baldwin & Nanson
Nanson drop every candidate at or below the average Borda score, each round Yes academic; some org elections Baldwin & Nanson

Two things worth underlining. First, Hare is the only one of these the US actually calls "RCV" — but it's also the one prone to center squeeze (eliminating a broadly-liked middle candidate who'd beat everyone head-to-head). Second, the Condorcet-safe variants (BTR, Baldwin, Nanson) fix that specific flaw precisely because they stop eliminating purely on first-choice counts. (Borda and Coombs read whole ballots but are not Condorcet methods; BTR/Baldwin/Nanson are.)

Where does Ranked Robin fit? It doesn't eliminate at all — RCV-RR (Ranked Robin / Copeland) compares every pair head-to-head and elects whoever wins the most matchups. It's the round-robin alternative to sequential elimination. See Ranked Robin.

Same Hare rule, different results: the implementation knobs

Even two elections that both run plain Hare IRV can disagree, because real ballots force choices the textbook glosses over:

  • How many candidates you may rank. NYC allows 5; San Francisco long allowed only 3; Sri Lanka 3. A shorter ballot means more exhausted ballots (a ballot whose every ranked candidate has been eliminated), which changes the denominator and can change the winner.
  • Batch vs. one-at-a-time elimination. Dropping several hopeless candidates at once usually matches single elimination, but not always at the margins.
  • What "majority" counts against. A majority of continuing ballots (exhausted ballots excluded) vs. a majority of all ballots cast are different thresholds — the first is how most US IRV laws declare a winner.
  • Equal ranks and skipped rankings. Pure IRV forbids equal ranks; jurisdictions differ on whether a skipped rank ends the ballot or is passed over.
  • Tie-breaks. Who gets eliminated when two candidates are tied for last is set by statute (lot, prior round, etc.) and can flip a close result. Because ranks carry no strength signal, there's often little to break the tie with, so it falls to chance sooner than in a score method — see Tie-Breaking: STAR vs. RCV-IRV for why strict ranks make ties harder to resolve, not easier. The academic literature answers this differently from statute: it removes every candidate tied for last in one step — a third meaning of "batch elimination," distinct from the out-of-reach row above — which on a symmetric profile can empty the whole field and end the count in an all-candidate tie. See Batch elimination — what happens when the batch is everyone.

This is why a precise reference says not just "IRV" but the whole rule set — the elimination rule plus the ballot rules.

Multi-winner: the same Hare family, renamed STV

For several seats at once, the Hare idea becomes the Single Transferable Vote (STV) — proportional, not majoritarian. Instead of "win a majority," a candidate must reach a quota (the Droop quota, ⌊total ÷ (seats + 1)⌋ + 1); a candidate over quota is elected and the surplus above it transfers to next choices, while last-place candidates are eliminated and transfer downward, until every seat is filled. Run STV with a single seat and it reduces exactly to IRV-Hare — siblings, not separate inventions. (FairVote promotes IRV-Hare for one seat and STV for many; both are "RCV.")

So which label should I use?

Context Use
Everyday / public-facing (slides, intro talks, op-eds) RCV-IRV — clear enough; "(Hare)" is over-precise here
The elimination rule is the actual point (comparing variants, this page) RCV-IRV (Hare) — names the exact rule
Statutes, specs, academic papers, or any place a reader could assume Coombs/BTR/Baldwin RCV-IRV (Hare) + the ballot rules (rankings allowed, majority basis)
Multi-winner / proportional STV
The pairwise, no-elimination alternative RCV-RR (Ranked Robin)

Short version: insisting on bare RCV-IRV is right for everyday use — it already rules out STV, Ranked Robin, Approval, and STAR. Escalate to RCV-IRV (Hare) only when the elimination rule itself is on the table, because that's the moment "RCV-IRV" stops being specific enough.

Learn more — external resources